 About 3,700 results  books.google.com Quadratic Transformations The formulas 3.8(1—24) may be viewed as a
transformation of the 2F1 in the variable, actually a linear ... The basic formulas
are due to Gauss and Kummer and a complete list is due to Goursat; see Erdélyi
et al. 

 books.google.com 1662 Kummer's Function where 2F1(a, b, c, z) is the HYPERGEOMETRIC
FUNCTION with m #–1/2, 1, 3/2, ..., and T(z) is the ... Kummer's Function
CONFLUENT HYPERGEOMETRIC FUNCTION Kummer's Quadratic
Transformation A ... 

 books.google.com dimensional spaces of solutions of certain differential equations. In order to relate
them to each other, we must use Kummer's quadratic transformation formula. This
involves certain substitutions which lift the correlation functions of t = 22/21 to ... 

 books.google.com 8.18 Show that 2/ r(i[c + a])r(i[ca+ 1]) .19 Use (8.6.23) (with a and b interchanged
) to derive Kummer's quadratic transformation (6.1.11). .20 Show that / 1 1\ r(i[a +
*+l])r(i) F[a,b,[a + b+l]; » 2 2/ r(I[fl+l])r(I[6+l]) 8.21 Verify the identity (8.4.5). 

 books.google.com Quadratic Transformations In §5.4 we mentioned Kummer's 24 solutions of the
hypergeornetric differential equation. ... (1881) made a thorough study of another
kind of transformation, although the basic ideas are due to Gauss and Kummer. 

 books.google.com At the end of the second part of this paper Kummer wrote that he had tried to
extend his results to ... The rest of the quadratic transformations come from using
linear fractional relations and connections between three solutions of the ... 

 books.google.com (6,202) 2 4x3 Kummer's quadratic transformation formulas for the hypergeometric
functions give (see [1], 15.3.22) 1 1 Fi  –2 ji , –2 j2; – — ji – j2; —— 2 ( J1 J25 2
J1  J2 :) 1 1 \* = 2 Fl (    ( #) ) • (6.203) 2 2x3 Now for any 6 Ji ..J2 ji y y  • y ... 

 books.google.com Linear, Quadratic and Cubic Transformations PfajfKummer transformations: 2F1
<a, b; C; 1) = (1—Z)—a2F1 (4, cb; C; L) <19) z—1 (c<,:25; arg(1—z) §7T—€ (0
<€ <rr)); 2F1<a, b; C; 1) = <1 Z)_b2F1 <1», c 4; C; <20) Z (c˘Z6; arg(1—z) ... 

 books.google.com f. It is suflicient to find the coefficients in the relations connecting one set of six
forms, for then all the other relations can be deduced by operating on (x, y, z, t)
with the transformations of the group. § 16. QUADRATIC RELATIONS. Another ... 

 books.google.com In Pfaff ,s transformation. (2.2.6) c change x to x/b and let b > oo to get Kummer,s
first transformation, (4.1.11) A similar procedure applied to the quadratic
transformation, leads to Kummer,s second transformation, a •+ •" ' (4,U2) Finally,
the ... 

 